# THE LACUNARY STRONG ZWEIER CONVERGENT SEQUENCE SPACES

• Sengonul, Mehmet (Department of Mathematics, Nevsehir University)
• Published : 2010.01.31
• 82 6

#### Abstract

In this paper we introduce and study the lacunary strong Zweier sequence spaces $N_{\theta}^O[Z]$, $N_{\theta}[Z]$ consisting of all sequences x = $(x_k)$ such that (Zx) in the space $N_{\theta}$ and $N_{\theta}^O$ respectively, which is normed. Also, prove that $N_{\theta}^O[Z}$, $N_{\theta}[Z}$, are linearly isomorphic to the space $N_{\theta}^O$ and $N_{\theta}$, respectively. And we study some connections between lacunary strong Zweier sequence and lacunary statistical Zweier convergence sequence.

#### Keywords

lacunary sequence;Zweier space;statisticial convergence;Banach space;isomorphism

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